When a 3-phase induction motor is supplied with balanced 3-phase supply, it produces a rotating magnetic field of magnitude:

Rotating Magnetic Field in a 3-Phase Induction Motor

Definition: A 3-phase induction motor is a type of electric motor that operates on the principle of electromagnetic induction. When a balanced 3-phase supply is provided to the stator windings of the motor, it produces a rotating magnetic field (RMF). This RMF plays a crucial role in inducing current in the rotor and generating torque.

Working Principle: When the balanced 3-phase currents flow through the stator windings, they create three individual alternating magnetic fluxes that are spatially displaced by 120° in terms of physical placement and electrically displaced by 120° in terms of phase. These fluxes combine to form a single resultant magnetic field that rotates at synchronous speed. The magnitude of this resultant rotating magnetic field is determined by the peak value of the flux due to any individual phase.

Magnitude of the Rotating Magnetic Field:

The resultant flux (Φ_r) of the rotating magnetic field is calculated as:

Φ_r = √(Φ_A² + Φ_B² + Φ_C²)

Here, Φ_A, Φ_B, and Φ_C are the instantaneous fluxes of each phase. Since the three phases are balanced and displaced by 120° from each other, the resultant magnetic field is constant in magnitude and rotates at synchronous speed.

The key point is that the magnitude of the resultant rotating magnetic field is 1.5 times the peak value of the flux due to any individual phase. This result is derived based on the vector addition of the three-phase fluxes.

Correct Option Analysis:

The correct answer is:

Option 3: 1.5 times the peak value of the flux due to any individual phase.

This is the correct option because, in a balanced 3-phase system, the rotating magnetic field generated in the air gap has a magnitude that is 1.5 times the peak flux of any individual phase. This relationship is a fundamental characteristic of the 3-phase induction motor’s operation and is critical for its performance.

Additional Information:

To better understand the analysis, let us evaluate why the other options are incorrect:

Option 1: Twice the peak value of the flux due to any individual phase.

This option is incorrect because the resultant magnetic field is not twice the peak value of any individual phase flux. The correct relationship, as discussed, is 1.5 times the peak value of the flux due to any individual phase, not 2 times.

Option 2: Equal to the peak value of the flux due to any individual phase.

This option is incorrect because the resultant magnetic field is not merely equal to the peak value of any individual phase flux. Instead, it is 1.5 times the peak value, as derived from the vector addition of the three-phase fluxes.

Option 4: 0.5 times the peak value of the flux due to any individual phase.

This option is incorrect because the resultant magnetic field is not half of the peak value of any individual phase flux. The correct relationship is 1.5 times the peak value.

Option 5: (Not provided in the question)

Since no additional option is provided, it does not apply to this analysis.

Conclusion:

In a 3-phase induction motor, when a balanced 3-phase supply is provided, the motor produces a rotating magnetic field with a magnitude of 1.5 times the peak value of the flux due to any individual phase. This characteristic plays a pivotal role in the operation of the motor, ensuring efficient energy conversion and torque production. Understanding this fundamental principle is essential for analyzing and designing 3-phase induction motors.